Next, we introduce the cohomology of a relative Rota-Baxter algebra with coefficients in a bimodule. The cohomology of a relative Rota-Baxter algebra introduced in [1]} turns out to be the cohomology of the relative Rota-Baxter algebra with coefficients in the adjoint bimodule. Then we consider abelian extensions of a relative Rota-Baxter algebra by a bimodule. We show that isomorphism classes of such abelian extensions are classified by the second cohomology group (cf. Theorem REF ).
